Wave
making resistance is a form of drag
that effects surface Watercraft, such as boats
and ships, and
reflects the energy required to push the water out of the way of the
hull. This energy goes into creating the wake.

Physics

Graph
of wave-making resistance of a displacement hull, with a mark at a
speed/length ratio of 1.34

For
small displacement hulls, such as sailboats or rowboats, wave making
resistance is the major source of drag. The unique properties of
deepwater waves (where the water depth is deeper than the half the
wavelength) mean that the wave making resistance is very dependent upon
the hull's
interaction with the wake.

The
propagation speed of deepwater waves is proportional to the square root
of the wavelength of the generated waves, and the wavelength of a boat's
wake is based on its waterline length — so: there is a direct
relationship between the waterline length (and thus wave propagation
speed) and the rate at which drag increases.

A
simple way of considering wave-making resistance is to look at the hull
in relation to its wake. At speeds lower than the wave propagation
speed, the wave rapidly dissipates to the sides. As the hull approaches
the wave propagation speed, however, the wake at the bow begins to build
up faster than it can dissipate, and so it grows in amplitude. Since the
water is not able to "get out of the way of the hull fast
enough", the hull, in essence, has to climb over or push through
the bow wave. This results in an exponential increase in resistance with
increasing speed.

To
calculate the speed of wave propagation, the following formula is used:

Plugging
in the appropriate value for gravity and solving yields the equation:

Or,
in metric units:

These
values, 1.34 and 2.5, are often used in the hull
speed rule of thumb used to compare potential speeds of displacement
hulls, and this relationship is also fundamental to the Froude
number, used in the comparison of different scales of watercraft.

When
the vessel exceeds a speed/length ratio of 0.94, it starts to outrun
most of its bow wave, the hull actually settles slightly in the water as
it is now only supported by two wave peaks. As the vessel exceeds a
speed/length ratio of 1.34, the hull speed, the wavelength is now longer
than the hull, and the stern is no longer supported by the wake, causing
the stern to squat, and the bow rise. The hull is now starting to climb
its own bow wave, and resistance begins to increase at a very high rate.
While it is possible to drive a displacement hull faster than a
speed/length ratio of 1.34, it is prohibitively expensive to do so. Most
large vessels operate at speed/length ratios well below that level, at
speed/length ratios of under 1.0.

Ways
of reducing wave making resistance

Since
wave making resistance is based on the energy required to push the water
out of the way of the hull, there are a number of ways that this can be
minimized.

Reduced
displacement

Reducing
the displacement of the craft, by eliminating excess weight, is the most
straightforward way to reduce the wave making drag. Another way is to
shape the hull so as to generate lift as it moves through the water.
Semi-displacement hulls and planing hulls do this, and they are able to
break through the hull speed barrier and transition into a realm
where drag increases at a much lower rate. The downside of this is that
planing is only practical on smaller vessels, with high power to weight
ratios, such as motorboats.
It is not a practical solution for a large vessel such as a supertanker.

Fine
entry

A
hull with a blunt bow has to push the water away very quickly to pass
through, and this high acceleration requires large amounts of energy. By
using a fine bow, with a sharper angle that pushes the water out
of the way more gradually, the amount of energy required to displace the
water will be less, even though the same total amount of water will be
displaced. A modern variation is the wave-piercing design.

Bulbous
bow

A
special type of bow, called a bulbous bow, is often used on large
motor vessels to reduce wave making drag. The bulb alters the waves
generated by the hull, but due to its very limited range of effect, is
only useful on large motor vessels operating at constant speeds.

Semi-displacement
and planing hulls

A
graph showing resistance/weight ratio as a function of
speed/length ratio for displacement, semi-displacement, and
planing hulls

Since
semi-displacement and planing hulls generate a significant amount of
lift in operation, they are capable of breaking the barrier of the wave
propagation speed and operating in realms of much lower drag, but to do
this they must be capable of first pushing past that speed, which
requires significant power. Once the hull gets over the hump of
the bow wave, the rate of increase of the wave drag will start to reduce
significantly.

Wave
Piercing Hulls

A
wave-piercing boat hull has a very fine bow, with reduced
buoyancy in the forward portions.

When
a wave is encountered, the lack of buoyancy means the hull pierces
through the water rather than riding over the top - resulting in a
smoother ride than traditional designs, and in diminished stress on the
vessel and crew. It also reduces a boat's wave making resistance.

Design
theory calls for very long thin hulls, so in practice most are
multi-hulls such as catamarans.

The
main current usage areas are passenger ferries
and military craft.